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(5) Let f (x1, F2) = (2 + 4 (x1)° , 3x2 , 1122) (a) What are the component functions of f? (b) Let a = (0, 1). What is b = f (a)? (c) Use Calc3 to give the Jacobian matrix of f at a. (d) Prove using the (limit!!) definition of the (total) derivative that Dfg is equal to your answer in part (c)

(5) Let f (x1, F2) = (2 + 4 (x1)° , 3x2 , 1122) (a) What are the component functions of f? (b) Let a = (0, 1). What is b = f (a)? (c) Use Calc3 to give the Jacobian matrix of f at a. (d) Prove using the (limit!!) definition of the (total) derivative that Dfg is equal to your answer in part (c)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 5

(5) Let f (11, 12) = (2 +4 (r1)² , 3x2 , 1123) (a) What are the component functions of f? (b) Let a = (0, 1) . What is b = f (a)? (c) Use Calc3 to give the Jacobian matrix of f at a. (d) Prove using the (limit!!) definition of the (total) derivative that Dfa is equal to your answer in part (c) (6) Continuing, we let g (y1, Y2; Y3) = 6y1 – 5y2 + 3y3 (a) Use the fact that g is linear to give the total derivative of g at b in matrix form. (b) Use the chain rule to compute the (total) derivative of (gof) at a using ONLY parts (1d.) and (2a.).
Transcribed Image Text:(5) Let f (11, 12) = (2 +4 (r1)² , 3x2 , 1123) (a) What are the component functions of f? (b) Let a = (0, 1) . What is b = f (a)? (c) Use Calc3 to give the Jacobian matrix of f at a. (d) Prove using the (limit!!) definition of the (total) derivative that Dfa is equal to your answer in part (c) (6) Continuing, we let g (y1, Y2; Y3) = 6y1 – 5y2 + 3y3 (a) Use the fact that g is linear to give the total derivative of g at b in matrix form. (b) Use the chain rule to compute the (total) derivative of (gof) at a using ONLY parts (1d.) and (2a.).
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